Wave filter



W. H. MARTIN.

WAVE FILTER.

APPLICATION FILED APR.2B. 1920. 1,434,555, Pianted NOV. 7, 1922.

Fraqaeway I N V EN TOR. BY wi /11mm MERNEY Qggg Nov. 7, il2f2.

WILLIAM H. DEAR/TIN} (31 NEW YORK, N. 53.,

ASSIGNOR T0 AMERICAN TELEPHONE AND WAVE Application filed April 26, 1929.

To (17/ 'uhomif "HNLj/ concern Be it known that lali iiaiiam l-l. MARTIN, residing at New York. in the county of Bronx and State of New York, have invented certain improvements in Wave Filters, oi which the 'lollowiug is a s ecificat1on.

Mv invention relates to wave filters for use electric circuits where it is desired to transmit alternating current of selected frequencies and to suppress, orpartly suppress, currents of other frequencies. More particularlv it concerns wave filters of the general type illustrated and described in the patents to George A. Campbell, 1,227,113 and 1.221114 issued May 252., i917.

lhe present invention proposes a filter which freely transmits all frequencies in a range between certain pie-assigned limits, neither of which is zero or infinity, and which attenuates frequencies outside this range. The filter of the present invention is characterized by having theoretically infi-- nite attenuation at a finite frequency other than zero and lying in the attenuated range. it may consequently be so designed that 1t will effect substantially complete suppression of any desired frequency outside the transmitted band, or it may be so proportioned. that the frequency of infinite attenuation is close to either limit of the transmitted band, so that a very sharp cut-off action may be attained at the said limit. As in the Campbell filters. all frequencies within the attenuated range can be suppressed to any desired degree by use of a sufiiciently large number of sections. The special feature of this filter, however, lies in the fact that the attenuation per section is substantially infinite for one frequency which can be freely chosen within the specified limits.

A good understanding of the invention may now be had from the following description of one form of embodiment thereof, reference being had to the accompanying drawin in which,

igure 1 is a diagrammatic View showing one form of embodiment of the invention;

Figs. 2 and 3 are diagrams showing graphically the attenuation characteristics of the filter of Fig. 1; and

Fig. 4 is a diagrammatic View showing one form of termination of the filter.

Serial No. 32 8,76 3.

ture which distinguishes them from the lilters disclosed in the Campbell patents hereinbetore referred to, in certain of which filters the series impedances consist of series resonant circuits and the shunt impedances,

of parallel or anti-resonant circuits.

1 have found that the type of filter of this invention has certain advantageous characteristics which l shall presently explain with reference to Figs. 2 and 3, which show graphically the attenuation of filters similar to that of Fig. 1, the abscissae representing frequencies and the ordinates, values of attenuation. The curve of Fig. 2 shows the attenuation for the general case in which the numerical product of L times C is smaller than that of L times C and that of Fig. 3, the attenuation when the reverse is true. It will be observed that the attenuation is nil only for the band of frequencies lying between f and f this being the transmitted band. The attenuation is a maximum at the frequency f being theroretically equal to infinity. When is close to i the slope of the attenuation curve through f is very steep showing that the filter discriminates sharply against frequencies just outside the transmitted band. By so designing the filter that f is above i (Fig. 2) the sharp-cut-ofi may be attained for the upper limit of thetransmitted band, and by so proportioning the impedances that f is below f (Fig. 3) the same property may be secured for the lower limit. Moreover, where it is desired to discriminate particularly against some pie-determined frequency outside the transmitted band, the filter may be so designed that it has infinite attenuation for this freuency, provided there is no energy dissipat1on in the filter.

I shall now give certain convenient mathematicalformulae by means of which any one skilled in the art may design a filter of the type disclosed herein, to meet the requirements in any particular practical case.

The design of the filter involves the derivation of the values of the four constants L L (1 and C These values may of course, be chosen at will, and the properties of the filter computed therefrom, but in the Y general case the reverse procedure will be more convenient, i.e., to choose the pro er v ties of the filter (according to the conditions third as f the frequency of infinite attenuation, and the fourth, as the impedance of the filter, this factor being, of importance because it is desirable to make the same substantially equal to that of the circuit into which the filter is placed, in order that reflection losses may be avoided. lhe relations which exist between the above-mew tioned, properties of the filter and the quantities L L C, and .C. will now be set out in mathematical form.

In the Campbell patents hcreinbefore mentioned, it was shown (equations 3 and i) that for a periodic structure of the type now under consideration, in which the series impedance per section is Z, and the shunt impedance per section is Z there is unattenuated transmission for all frequencies of current for which the value of l/2 %)+lliesbetweeni1, 1

so that the limiting values f and f of the frequencies for free transmission may be determined from the following equations:

In the present case the values of Z and Z in terms of frequency are ar i Z1 h IL 1 P214101 L i 2 1 as given b (3) and (4), are substituted in equation the resultant expression may be solved for 12, one of the roots, 1),, determining one limiting frequency, f,,, and the other, 2 the other limiting frequency, f

COSll I=l/2%- +l= co 21 P 2 2 L 1 11 L 6 When solved for 7;, this gives The frequencies 71,, f and f, are thus expressed in terms of the constants of the filter. It remains to evolve an expression for the impedance of the filter.

This impedance varies with frequency, and it has been found convenient in the art to specify in design the impedance at the frequency, termed mid-frequency, which is the geometric mean of the limiting frequencies of the transmitted range, i. e., The impedance of a filter or any similar periodic structure varies also according to the termination of the structure and it therefore is important to specify the termination which is to he used. I shall for sake of illustration employ the mid-series termination for the present design formulae. It is to be expressly understood, however, that the invention is not limited to any particular type of termination.

A filter is defined to have mid-series termination when it is terminated by a series impedance of half that of the normal series section. This is illustrated in Fig. 4 in which the normal series impedance is Z and the left terminal impedance is %Z,, i. e.. com posed of 11L, and 2G,. The filter may be assumed to have an infinite number of sections toward the right so that the impedance at any other mid-series section, such as that which extends to theright from line 1-1 is the same as the impedance measured at the ncense terminals w-b. Consequently, if 7;, designates the mid-series section impedance substituting for Z, and Z their values as given by equations (3) and (4c), and simplifying, it will be found that the impedance at the frequency f isv given by the exe n n+iL2 2 2 Although tl e above expression is derived for a filter having an infinite number of sections, it is substantially correct for one having only a few sections irovided the same is shown so as to be approxima mly the same as that of the line to which the filter is connected. For mid-series termination the two terminal sections of the filter should,

p ression however, be alike i. e. in the present instance both terminations should be mid-series.

Equations (5), (G), (7) and (10) are four simultaneous equations involving the factors 1),, 1p 32,, and Z the values of which may be assumed, and the factors lg, L C, and C. the values of which are to be determined. These equations may therefore be solved for the values of the last mentioned quantities, and when this is done it will be found that ms o -tat T anial Z msc f an) (2 3 P3) Z z oll Substituting these values in equations 11) to (14), and solving gives:

i .0542 henries L 1. 33 henries C .0884 microfarads C .119 microfarads i fill as the constants of the normal filter section.

With the mid-series termination assumed herein the values of the first and last series inductance and capacity are, respectively, .OZTl henries and .1768 microfarads.

Although l have herein shown and described only one form and arrangement of apparatus embodying my invention, it is readily understood that various changes and modifications may be made therein within the scope of the following claims without departing from the spirit and scope of the invention. 1

llhat I claim is:

1. A wave filter for an electric circuit, said filter having a plurality of like recur rent sections, each section comprising lumped impedence consisting of a parallel resonant circuit in series with the said electric circuit and lumped, impedance, consisting of a parallel resonant circuit, adjacently in shunt thereto, said impedances being so proportioned that the filter approximately suppresses all frequencies lying outside a preassigned band extending between two we frequencies other than zero or infinity and substantially completely suppresses a certain pr assigned finite frequency other than zero.

2. A wave filter for an electric circuit, 11o said filter having a plurality of like recurrent sections, each section comprising a par allel resonant circuit in series with the said circuit and a parallel resonant circuit adjacently in shunt thereto, the impedances of 31.155 said circuits being so proportioned that the filter transmits freely all frequencies lying, within two limiting frequencies other than zero or infinity but approximately suppress es the frequencies outside of the said limi-t- 12o ing frequencies and discriminates sharply against frequencies close to one of said limits,

3. A Wave filter for an electric circuit, said filter having a plurality of like recurrent sections, each section comprising a lumped inductance and capacity in parallel with each other inserted in series with the circuit and a lumped inductance and capacity in parallel with each other connected in shunt to the circuit, adjacently to said firstinentioned inductance and capacity.

'4. The combination with a line, of a filter composed of a plurality of periodically recurring sections, each of which consists of a parallel resonant circuit connected in series with the line and a parallel resonant circuit connected in shunt thereto.

5. A wave filter for an electric circuit said filter having a plurality of like recurrent sections, each sectlon comprising a resonant circuit in series with the circuit and a like type of resonant circuit in shunt to the circuit, each of which resonant circuits comprises lumped inductance and capacity connected in parallel with each other, the values of which are determined by a finite frequency other than zero at which the attenuation of the filter is theoretically infinite, the impedance of the filter and the limiting frequencies of a preassigned band of free transmission, which limiting frequencies are other than zero or infinity.

6. A Wave filter for an electric circuit, said 'filter having a plurality of like recurrent sections, each section comp-rising lumped impedance in serieswith the circuit and lumped impedance in shunt thereto the said impedances consisting of arallel resonant circuits so proportioned t at the attenuation of the filter has a finite value at a chosen finite frequency and decreases, as the frequency is changed in one direction, until it is substantially equal to zero at a certain other finite frequency, remains at this value until still another finite frequency is reached, then increases until it becomes theoretically infinite at still another finite frequency and then decreases with further change of frequency in the same direction.

7. A wave-filter for an electric circuit, said filter having a plurality of like recurrent sections, each section consisting of a parallel combination connected in series with the line and resonant at a certain frequency, and another parallel combination connected in shunt to the line and resonant at a certain other frequency.

In testimony whereof, I have signed my name to this specification this 23rd day of April 1920.

WILLIAM H. MARTIN. 

